Solid-State NMR: Principles

P. K. MadhuDepartment of Chemical Sciences

Tata Institute of Fundamental ResearchHomi Bhabha Road

ColabaMumbai 400 005, India

Solid-State NMR

Matter

Gas Liquid Solid

Isotropic Anisotropic

Ordered Disordered

MembraneCrystals Fibrils Glasses

Biological materials

Targets for SSNMR

Membrane proteins

Rhodopsin, Gramicidin, …….

Targets for SSNMR

β-Amyloid fibrils

Targets for SSNMR: Biology

• Lipid bilayers

• Membranes reconstituted with different additives such as cholesterol, drugs or peptides

• Structure analysis of membrane-active peptides, ion channels, and receptors

• Amyloid fibrils, silk, and elastic proteins

Difficulties

•Restricted or no internal motion, unlike solution-state

•All interactions present in toto

•Interactions are anisotropic leading to broadeningof spectral lines

•Plethora of information present, leading to a completecharacterisation of materials

Reality

Simple 1D solution-state spectrum1H spectrum of a protein

Simple 1D solid-state spectrum13C spectrum of glycine

Remedies

• Mimick the inherent averaging processes in solution-state to obtain high-resolution, isotropic information

• Goal #1:(Resolution and Sensitivity): Remove anisotropic parts and retain only isotropic parts: Decoupling

• Goal #2:(Let us have the cake and eat it as well) Get backthe anisotropic parts for elucidation of geometry parameters: Recoupling

Remedies

Anisotropic Part

Spatial Part

Spin Part

Independent:Can be individuallymanipulated

Mechanical manipulation

RF manipulation

Hamiltonians and their Manipulation

[ ] isotropiccanisotropiSPINSPACETOTAL Η+Η⊗Η=Η

•Rotating the crystallites in a given powder •Sample spinning: Mechanical manipulation

•Easier to visualise•Difficult to implement

Spatial Part: Manipulation Spin Part: Manipulation

•Rotating the spins in a given powder •Spins rotation: Manipulation by RF pulses•Easier to Implement•Difficult to visualise

Which Angle to Roate at?

Spatial part of the anisotropic Hamiltonian

)1cos3(2/1

)(cos

2

2

−θ

θP

0 100 200 300-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

P2(cosθ)=0 for θ=54.70

54.7

B0

SAMPLEROTATION

Average out the chemical shift anisotropy, to achieve good

sensitivity and resolution

Magic-Angle Spinning (MAS)

Averages out the chemical shift anisotropy, to achieve good

sensitivity and resolution

Magic-Angle Spinning (MAS)

θ=54.7

13C spectra of [13C2]-glycine

no spinning

with MAS at 12 kHz

+H3NC

H H

O

O-

Resolution and Sensitivity Enhancement by MAS

Magic-Angle Spinning Spectra: Resolution Enhancement

Glycine

The powder pattern breaks up into a centreband and sidebands spaced at integer multiples of the rotor frequency

14 kHz

8 kHz

5 kHz

3 kHz

1181 Hz

Static

Chemical Shift δ/ (ppm)50 0100150200250

MAS Rotor TypesMAS Rotor Types

Rotor caps

ZrOZrO22 MacorMacor BNBN KelKel--FF VespelVespel

Standard Bore MAS ProbeStandard Bore MAS Probe

stator flip mechanism

bearing gas inlet

RF electronics

BN stator

proton trap

RF coil

Abundant and Rare Nuclear Spins

Rare spins experience weaker homonuclear dipolar couplings, hence, the resolution limiting aspect is the heteronuclear dipolar coupling to the abundant 1H

13C, 15N…. 1H, 19F….

Heteronuclear Dipolar Decoupling

MAS RF

Decoupling

Homonuclear dipolarcoupling

Heteronuclear dipolarcoupling

Abundant spins1H

Rare spins13C, 15N

Typical 1H-13C coupling= -25 kHz

Heteronuclear Dipolar Decoupling

Decoupling

(π/2)y

S

I1H

13C

MAS RF

Decoupling

S spin detection

15202530354045505560 ppm

MAS + Heteronuclear Dipolar Decoupling

Static

Static+Decoupling

MAS

MAS+Decoupling

13C spectra of adamantane

MAS + Heteronuclear Dipolar Decoupling

2-13C Glycine5 kHz broadening

334 Hz broadening

80 Hz broadening

CW decoupling at 150 kHzMAS at 30 kHz

Only decoupling

Only MAS

MAS+Decoupling

Cross Polarisation, CP

ωI ωS

½

-½

-½

½

Laboratory frame

ωI ωS

½

-½ -½

½

Doubly rotating frame

Energy levels of both nuclei are matched in the doubly rotating frame.A spin-lock RF field is equivalent to producing a rotating-frame transformation.Hence, we need a continuous spin-lock RF field on both the nuclei for CP.

A match of the energy levels is produced when the nutationfrequencies of both the spins along the effective RF field direction are the same: B1I=B1S or in other words γIωI=γSωS

Hartman-Hahn condition

CP Pulse Sequence+Decoupling

Decoupling

S

I1H

13C

90x y

CP

CP

CPMAS, basic pulse block in solid-state NMR for both sensitivity and resolution

MAS and heteronuclear decoupling lead to resolutionCP leads to sensitivity

CP contact time

RF fields adjustedfor Hartman-Hahn condition

Magnetisation transfer

CPMAS Spectrum

*Enhanced signal,~γI/γS

*T1 of abundant high-γ nucleishorter than that of the rare low-γ nuclei

*Spatial proximity

Decoupling

S

I1H

13C

90x y

CP

CP

ΔωnutS=2−3ωr

B0

SAMPLEROTATION

CPMAS

The routine way towards high-resolution and sensitivityin solid-state NMR experiments

θ=54.7

Stejskal, Schaefer, Waugh, JMR, 18,560,1975Stejskal, Schaefer, Waugh, JMR, 28,105,1977

SOLID STATE NMR

Selection rules may be generated at will

RF Field

Sample Rotation

B , Static Magnetic Field0

Electromagnetic irradiation >> internal coupling strengthsSpatial+Spin External Dynamic

Symmetry

Recoupling under Magic-Angle Spinning:Retrieving Lost Interactions

What is Recoupling and Why Recoupling

Solid-state NMR Solution-state NMR

Anisotropic interactionswith geometry information

CSA: Local chemical environmentDD: Distances and anglesQuad: Local environment, asymmetry,

distribution

Only isotropic information areinherently present

Geometry information availableindirectly via relaxation experiments

Direct manifestation of geometry parametersProblem: High-resolution schemes kill

the anisotropy and geometry information

Question: Can the lost anisotropic interactionsretrieved whilst retaining the isotropic resolution?

Having the cake and eat it too!

Recoupling in Solution State

Recoupling is done in solution-state NMR, NOE for example

Rapid molecular motions modulate the dipole-dipole interactionsand the fluctuating dipolar fields can drive magnetisation exchange(or cross relaxation) between spins over a wide range of chemicalshifts

This mechanism fails in solid state due to the restricted molecularmotions that cannot supply the energy differences necessary formolecular motions (also resolution and sensitivity considerations play a role)

Recoupling of Interactions

Rigid Solid MASRF Irradiation:Recouplinginteractions

Resolution, butInformation sacrificed!

Both resolutionand geometryinformation

Hetero/Homonuclear Recoupling

Pay a price: A scale factor!

Couplings may be reintroducedfor certain periods of the experiment

Sequence Zoo

DRAMA

MELODRAMA

RFDR

SEDRA

SEDOR

REDOR

CNnν

RNnν

USEME

RIL

R2

R3HORROR

DARR

BABA

DRAWS

ωr = 5000 Hzωiso= 5000 Hz

0 2500-2500

-2500 0 2500

Rotational Resonance

ωr = 3000 Hzωiso= 5000 Hz

Raleigh et al., Chem. Phys. Lett. 146, 71, 1988

The splitting indicatesthe strength of the dipolar couplingbetween the two spins

Rotational Resonance Condition:Δωiso=n ωr

Correlation Spectrum :RFDR

[U-13C-15N]achatin-II16 π pulsesMAS 10 kHz

Being used currently in biomolecules for 13C-13C correlation towards assignments

RFDR: SH3 Domain Protein

Pauli et al., J. Magn. Reson. 143, 411, 2000

Secondary Structure Elements

Backbone conformation by correlating two anisotropic interactionssuch as CSA or DD

Interactions measured from 2D experiments:Recoupling, double-quantum methods

Structure by Solid-State NMR: Schematic

Assignments in Solid-State NMR: Example

α-spectrin SH3 domain

NCACB

Correlation Experiments: HNCA in Solid-State

15N-α-Spectrin SH3 domain 1H-15N HSQC (dipolar). 17.6 T, MAS 8 kHz

1H-15N-13C HNCA 9.4 T, MAS 8 kHz J. Biomol. NMR, 25, 217, 2003

Sample Preparation Issues

Martin and Zilm, J. Magn. Res., 165, 162, 2003

Ubiquitin

polycrystalline

nanocrystalline

lyophilised

Sample Preparation Issues

Pauli,….,Oschkinat, J. Biomol. NMR, 25, 217, 2003

Lypholised from aqueous low-salt buffer

Lypholised from aqueous low-salt buffer+adding water

Lypholised from a solution also havingPEG and sucrose

Precipitated from a rich ammoniumsulphate solution

SH3 domain protein

Proteins in Solid-State NMR

Membrane proteinsAmyloid fibrilsSH3 domain proteinUbiquitinBacillus Subtilis protein Crhα-Synuclein

Sequential Assignment and Conformational Analysis

2*10.4 kDa dimeric form ofThe Bacillus Subtilis protein Crh

Bockmann,….,Baldus, J. Biomol. NMR, 27, 323, 2003

Sequential Assignment and Conformational Analysis

Bockmann,….,Baldus, J. Biomol. NMR, 27, 323, 2003

Conclusions

•Solid-state NMR has come of age

•A rich pasture for spin gymnastics and choreography

•A judicious combination of MAS and RF very vitalfor most experiments

•Selective manipulation of each spin interaction possible

•The methods in vogue now are being used to develop toolsto do solution-state kind of experiments for assignmentsin biomolecules

• Remarkable progress already made in various biomolecularsystems